Micro-electro-mechanical system (MEMS) membrane-type mirrors are well known and may be employed as an economical alternative to conventional deformable mirrors, which for example may utilize PZT (lead zirconium titanate) or PMN (lead magnesium niobate) actuator types. MEMS actuators generally utilize electrostatic attraction to deform the shape of the membrane mirror in a controllable manner. However, in contrast to PZT or PMN actuators, the relationship between the applied voltage and the membrane position with an electrostatic actuator is nonlinear.
For MEMS membrane-type mirrors, if the applied voltage is increased beyond a certain value, the electrostatic attraction exceeds the membrane's restoring force, which typically results in a condition referred to as “snap down.” When the membrane comes in contact with the underlying electrical plate (during the snap down event), the resulting spark discharge usually causes the rupture of the membrane. Consequently, to reduce the possibility of snap down, the maximum possible voltage to the actuator is generally limited to a safe value. However, one drawback of this limitation is that the speed and stroke of the actuator is reduced, resulting in a reduced bandwidth or a reduction in wavefront correction capability.
Another difference is that the “stiffness” of the electrostatic actuator may be less than PZT or PMN actuators. For example with PZT or PMN actuators, it may be assumed that actuator position is directly proportional to the applied voltage, regardless of any perturbing forces. With electrostatic actuators, the lack of stiffness may result in a greater position error due to perturbing forces, such as for example mirror membrane vibration or adjacent actuator cross-coupling. Position feedback sensing of the membrane is generally required to compensate for the inherent nonlinearity and lack of stiffness associated with the electrostatic actuators. The position feedback sensing is typically performed optically by using interferometers or wavefront sensors that are often expensive and prone to alignment problems. As a result, there is a need for improved techniques for position feedback sensors, such as for example for the MEMS membrane-type mirrors.